Mølmer-Sørensen Gate
The native entangling gate of trapped-ion processors, driving two or more ions through a shared motional mode.
Definition
The Mølmer-Sørensen (MS) gate entangles ions by applying bichromatic laser fields that couple their internal spin states to a shared vibrational mode of the ion crystal. To first order it realizes exp(-i θ (X⊗X) / 2) — an RXX gate — and returns the motional mode to its starting state at the end, so the phonons act only as a bus.
Matrix (θ = π/2)
This is RXX(π/2), locally equivalent to CNOT. A pair of single-qubit rotations before and after converts it into a standard CNOT for circuit compilers.
Why it is native
Ions do not interact directly; the MS scheme is the physically efficient way to entangle them because it uses the collective motion as a mediator and is, to leading order, insensitive to the exact motional temperature. It also extends naturally to global gates that entangle many ions at once, which is unique to this platform.
Advantages and limits
- High fidelity, since the interaction is symmetric and the phonon bus is disentangled by design
- Native multi-qubit MS gates entangle a whole register in one shot
- Sensitivity to motional heating and laser intensity noise sets the practical error floor
- Slower than superconducting two-qubit gates, but with longer coherence times to compensate
Compilation
Compilers for ion hardware express all entanglement in MS/RXX and single-qubit rotations rather than CNOT, avoiding wasted dressing gates. See RXX and native gate sets.